Dynamic Capital Structure Adjustment and the Impact of Fractional Dependent Variables

Elsas and Florysiak (2013) analyze dynamic panel estimation with a fractional (i.e. bounded) dependent variable in the context of empirically testing capital structure theories with respect to the so-called speed of adjustment (SOA). The (dynamic) trade-off theory predicts that firms have a target debt ratio. The SOA measures how fast firms get back to this target after (exogenous) shocks to their leverage. The study shows by Monte Carlo and resampling experiments that commonly applied estimators for the SOA yield severely biased estimates as they ignore that the dependent variable is bounded between zero and one. A new unbiased estimator is proposed and tested, called the DPF (dynamic panel fractional) estimator.

On this homepage, we provide codes that allow interested researchers to replicate some of the results in Elsas and Florysiak (2013) and the Stata implementation that can be used in their own research projects. The Stata codes include

- XTDPF: A Stata implementation of the DPF estimator called xtdpf.

- Simulation Code: Stata code to replicate the Monte Carlo simulations in Elsas and Florysiak (2013) that illustrates the usage of xtdpf as well as the bias of alternative estimators in the context of fractional dynamic panel estimation.

- XTLD: A simple Stata implementation of the long-difference estimator by Hahn, Hausman and Kuersteiner (2007).

XTDPF Estimator

The DPF estimator uses a doubly-censored Tobit specification that allows for corner observations at both zero and one, with a lagged dependent variable and accounts for unobserved heterogeneity. The DPF estimator builds on the model of Loudermilk (2007) and allows for unbalanced panel data.

The Stata implementation consists of an ado-file and a help-file (download xtdpf.zip (ZIP, 5 KB)). For installation, these files need to be downloaded and copied into the Stata "..\ado\plus\x" system folder.

Please note that we have tested the Stata xtdpf implementation thoroughly (using Stata Version 11 on standard Win 7 personal computers), but cannot guarantee that it is error-free or functional, so this code is provided under the GNU General Public License. However, please do not hesitate to send us an email if you face any difficulties.

The help file also contains code for a Stata do-file, that

a) simulates one data set and runs DPF estimation

b) runs Monte Carlo simulations comparing SOA estimates from 100 replications.

To use this code, copy the code from the help window and paste it into the Stata do-file editor.

Note that all simulations are based on the data generating process of the DPF estimator, so it is no surprise that this estimator performs best in a statistical sense. However, the simulation allows to learn about the data generating process, provides test data with known characteristics and illustrates the bias of the standard fixed-effects (xtreg) and the Blundell/Bond (xtdpdsys) system GMM estimators as these are alternative estimators used in the capital structure literature which are implemented in Stata on default.

Extended Simulations / Paper Replication

We also provide a do-file (ZIP, 2 KB) which is an extended version of the simulation code described above. These simulations serve to replicate the paper’s key result and are based on the simulation design described in Section III.A of Elsas and Florysiak (2013). The simulation compares the bias of the DPF estimator and benchmark estimators and yields results similar to the results reported in Table 2.I, column 5, and Figure 2 (‘censored’) in Elsas and Florysiak (2013).

Please note that we also provide a Stata implementation of the long-difference estimator by Hahn, Hausman and Kuersteiner (2007) (xtld.zip (ZIP, 3 KB)). This code however has not been tested much for it is only intended to allow easy replication of the paper’s results. To install xtld, please copy the ado and the help-file into Stata’s "..\ado\plus\x" system folder (in analogy to installing xtdpf).

To also run the extended simulations the xtlsdvc estimator needs to be installed from the Boston College Statistical Software Components (SSC) archive. Xtlsdvc calculates the bias-corrected least-squares dummy variable (LSDV) estimator for dynamic panel data using the bias approximations in Bruno (2005) and is one benchmark estimator used in the recent capital structure literature.

Please note that for usability, the simulations use a more parsimonious setup than in the paper with N = 100 and T = 10 and 100 simulation runs, results with regard to biases, however, are similar. In particular, the results table should look similar to the following one:

Sim. runMeanStd.Dev.MinMax

Since the true SOA used to simulate the data is set to 0.2, the MC results illustrate that all estimators that do not take fractionality into account are significantly biased.

The code can easily be adjusted for other constellations of the number of time and individual observations as well as simulation runs. However, if you run the extended simulations with a large data set, the xtlsdvc-implementation from the Stata repository can become prohibitively slow in our experience (which is why we have used our own LSDVC-implementation in Matlab for the paper).


Bruno, G. (2005): Approximating the Bias of the LSDVC Estimator for Dynamic Unbalanced Panel Data Models, Economics Letters 87, 361-366.

Elsas, R., and Florysiak, D. (2013): Dynamic Capital Structure Adjustment and the Impact of Fractional Dependent Variables, forthcoming Journal of Financial and Quantitative Analysis (JFQA).

Hahn J., Hausman, J. and Kuersteiner, G. (2007): Long Difference Instrumental Variables Estimation for Dynamic Panel Models with Fixed Effects, Journal of Econometrics 140, 574-617.

Loudermilk, M. (2007): Estimation of Fractional Dependent Variables in Dynamic Panel Data Models with an Application to Firm Dividend Policy, Journal of Business and Economic Statistics 25, 462-472.